Timeline for Individual mathematical objects whose study amounts to a (sub)discipline?
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
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| Dec 12, 2010 at 16:15 | comment | added | Bill Johnson | But studying a Banach space involves understanding the structure of its subspaces. 'Course the corollary to the universality of $C[0,1]$ is that we will never understand the structure of $C[0,1]$ as a Banach space. | |
| Dec 12, 2010 at 6:35 | comment | added | Adam Hughes | I also agree, if you consider the Sobolev spaces and in particular the Hilbert-Sobolev spaces, they embed nicely into other spaces and by infinite dimensionality and separability the latter are isometrically isomorphic to $\ell^2$, but at the same time the ways to go between them isn't really easy to recover the structure of one from the other, especially trying to figure out $H^k=W^{k,2}$ from just knowledge of $\ell^2$. | |
| Dec 12, 2010 at 3:35 | comment | added | Peter LeFanu Lumsdaine | What @fedja said. I don’t think “all widgets embed into $X$” together with “widgets are a field of study” makes $X$ a field of study. This is the same sort of argument by which a few logicians, set theorists, category theorists, etc. (and, more often, students meeting these subjects for the first time) claim “logic (set theory, category theory) subsumes all other mathematics”. | |
| Dec 12, 2010 at 2:52 | history | made wiki | Post Made Community Wiki by Kim Morrison | ||
| Dec 12, 2010 at 2:06 | comment | added | fedja | Be reasonable! I also was tempted to post an answer starting with "Almost anything would really do (with reasonable interpretation). An analytic function/the unit disk; A convex set/the simplex in high dimension; A graph/$\mathbb Z^3$" and ending with "And that's definitely a community wiki type question, if it is a question at all, which I have strong doubts about. Even if you had asked for "a single proof of a single statement about a single object", you would be in almost equally bad shape", but then decided to find some criterion for a good answer here instead (not that I succeeded :(). | |
| Dec 11, 2010 at 23:33 | history | answered | Bill Johnson | CC BY-SA 2.5 |